I received my doctorate from the University of Cologne in 2022 under the supervision of
Sibylle Schroll.
Following that, I was a JSPS short-term postdoctoral research fellow at the University of Tokyo working with
Osamu Iyama from late May to late August 2022.
My research focuses on the representation theory of finite-dimensional algebras and combinatorics.
In the representation theory of finite-dimensional algebras I am particularly interested in
- higher homological algebra,
- maximal green sequences,
- stability conditions,
- relations with cluster algebras.
In combinatorics, I am particularly interested in
- partially ordered sets, especially the higher Bruhat and Stasheff–Tamari orders,
- polytopes and their triangulations, especially cyclic polytopes.
I am naturally interested in the interplay between these two areas too.
In my spare time, I like reading Iris Murdoch novels.
3/2023 |
A survey of congruences and quotients of partially ordered sets, arXiv. |
2/2023 |
A geometric perspective on the τ-cluster morphism category, (with Sibylle Schroll, Aran Tattar, and Hipolito Treffinger) arXiv. |
1/2023 |
A structural view of maximal green sequences, (with Mikhail Gorsky) arXiv. |
8/2022 |
Stability spaces of string and band modules, (with Sibylle Schroll, Aran Tattar, Hipolito Treffinger, and Yadira Valdivieso) arXiv. |
8/2022 |
Triangulations of prisms and preprojective algebras of type A, (with Osamu Iyama) arXiv. |
6/2021 |
The two higher Stasheff–Tamari orders are equal, arXiv. |
To appear |
Quiver combinatorics and triangulations of cyclic polytopes |
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Algebraic Combinatorics. arXiv. |
2/2023 |
The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders |
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Electronic Journal of Combinatorics. DOI, arXiv. |
10/2022 |
New interpretations of the higher Stasheff–Tamari orders |
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Advances in Mathematics. DOI, arXiv. |
9/2021 |
The combinatorics of tensor products of higher Auslander algebras of type A, (with Jordan McMahon) |
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Glasgow Mathematical Journal. DOI, arXiv. |
2/2023 |
A structural view of maximal green sequences |
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Algebra group seminar, University of Cologne |
12/2022 |
Cyclic polytopes and representation theory |
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Representation theory of algebras session, Canadian Mathematical Society Winter Meeting, Toronto |
11/2022 |
The higher Stasheff–Tamari orders on triangulations of cyclic polytopes |
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Séminaire du LaCIM, Université du Québec à Montréal |
11/2022 |
Cyclic polytopes and representation theory |
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Geometry and mathematical physics seminar, University of Birmingham |
11/2022 |
Cyclic polytopes and representation theory |
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Pure mathematics seminar, Lancaster University |
10/2022 |
Mutation in higher cluster categories |
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Seminar@Aarhus, Aarhus University |
9/2022 |
A structural approach to maximal green sequences |
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Silting theory, algebras and representations, Charles University, Prague |
7/2022 |
Algebraic interpretation of the higher Stasheff–Tamari orders |
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Representation theory and various issues on related topics, Research Institute for Mathematical Sciences, Kyoto University |
7/2022 |
Cyclic polytopes and higher Auslander–Reiten theory III |
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Tokyo–Nagoya algebra seminar, University of Tokyo and Nagoya University |
6/2022 |
Cyclic polytopes and higher Auslander–Reiten theory II |
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Tokyo–Nagoya algebra seminar, University of Tokyo and Nagoya University |
6/2022 |
Mutating cluster-tilting objects in (d + 2)-angulated cluster categories |
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FD seminar |
6/2022 |
Cyclic polytopes and higher Auslander–Reiten theory I |
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Tokyo–Nagoya algebra seminar, University of Tokyo and Nagoya University |
2/2022 |
Equivalence of maximal green sequences |
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Paris algebra seminar, Institut de Mathématiques de Jussieu-Paris Rive Gauche |
1/2022 |
The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders |
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Formal Power Series and Algebraic Combinatorics |
1/2022 |
An algebraic interpretation of the higher Stasheff–Tamari orders |
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Aachen–Bochum–Cologne Darstellungstheorie Seminar |
12/2021 |
Cyclic polytopes and higher Auslander–Reiten theory |
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Tokyo–Nagoya algebra seminar |
4/2021 |
The higher Stasheff–Tamari orders in representation theory |
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Paris algebra seminar, Institut de Mathématiques de Jussieu-Paris Rive Gauche |
3/2021 |
New interpretations of the higher Stasheff–Tamari orders |
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Diskrete Mathematik / Geometrie Forschungsseminar, TU Berlin |
3/2021 |
The Tamari lattice in representation theory |
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Junior Algebra Colloquium, University of Bristol |
I have translated a couple of papers of Carathéodory from German into English. I make no claim to any of the mathematics in these papers.
It is also not impossible that I have introduced errors in the process of translation.